Integrated Reasoning (0/12) 1%

350 students at High School High are currently enrolled in French, Spanish, or both French and Spanish. 230 students are currently enrolled in Spanish. In the table, identify the number of students currently enrolled in French and the number of students currently enrolled in both French and Spanish. The two numbers must be consistent with each other and with the constraints above. Make exactly one choice in each column. French French and Spanish (one each) 140 180 200 220 260 280

French: The correct answer is E. I said A. French and Spanish: The correct answer is A. I said D. Although you could draw a Venn Diagram or a Double-Set Matrix to answer this question, there is a formula we can use to save time. Suppose there is an overlap between two groups, group X and group Y. The total number of items equals the number of items in group X, plus the number of items in group Y, plus the number of items in neither, minus the number of items in both - because you double-counted them by adding X and Y. So here's the formula: X + Y + Neither - Both= Total We can say the same for this problem: Spanish + French + Neither - Both = Total We know the total number of students is 350 and the number of students currently enrolled in Spanish is 230. Furthermore, we actually know that none of those 350 students is taking neither French nor Spanish. 230 + French + 0 - Both = 350 French - Both = 120 We need to find 2 choices that differ by 120, with the larger number representing the total number of students currently enrolled in French, and the smaller number representing the number of student enrolled in both French and Spanish. 260 and 140 are the only numbers in the list that have a difference of 120.

The invented languages of Kurtish and of Laeglish both obey principles of vowel harmony within words, although in different ways. In both languages, the five vowels (a, e, i, o, and u) are classified either as brutish (a, o, and u) or as fragile (e and i). In Kurtish, every word that contains vowels can itself be classified as brutish or as fragile, according to the vowels it contains; there are no mixed-vowel words. In Laeglish, on the other hand, it is possible to have mixed-vowel words, but within Laeglish words, every consonant (non-vowel letter) or continuous cluster of consonants can only directly touch vowels of one type or the other. In the first column, select a word that, according to the constraints given, could be in the Laeglish language, but not Kurtish. In the second column, select a word that could be in neither language. Make only two selections, one in each column. Laeglish only/ Neither Word (one each) calzral fjp aphueitse brushmen qudxatroua hzziigri

Laeglish only: The correct answer is C. I got right. Neither Word: The correct answer is D. I said B. You are asked to figure out and apply these linguistic constraints to possible words. Let's start with the classification of vowels as "brutish" (a, o, and u) and as "fragile" (e and i). Kurtish has stricter rules about the separation of these vowels—only one kind can appear within any word. Since this is a simple constraint, let's apply it first. Which words fail this constraint? calzral - only a, brutish - passes fjp - NO vowels, but that's okay (see note below) - passes aphueitse - both brutish (a and u) and fragile (e and i) - fails, can't be Kurtish brushmen - both brutish (u) and fragile (e) - fails, can't be Kurtish (don't be fooled by the fact that brushmen sounds okay in English, though it's not an English word) qudxatroua - only brutish (a, o, and u) - passes hzziigri - only fragile (i) - passes So we know that our two answers must be in the middle, aphueitse and brushmen. One of these could be Laeglish; the other cannot. Now we have to apply the second constraint, the one about Laeglish: every consonant or group of consonants can only "directly touch" vowels of one type or the other. Let's compare: aPHueiTSe - the PH touches a and u, which are both brutish - the TS touches i and e, which are both fragile This passes the Laeglish test. Double-check the other word: BRuSHMeN - the BR only touches u, but the SHM touches u (brutish) and e (fragile). That breaks the Laeglish rule. So aphueitse could be Laeglish but not Kurtish; brushmen could not be either. Note that fjp does not have any vowels as defined above, but no constraint demands that a word in either language contain vowels! In fact, a nod is given to the possibility of zero vowels within a word with the language "according to the vowels it [a word] contains, if any" (emphasis added). Don't apply outside knowledge inappropriately here (you expect words to have vowels).

10. Graph

Refer to MGMAT

11. Graph

Refer to MGMAT

3. Graph

Refer to MGMAT

4. Graph

Refer to MGMAT

6. Graph

Refer to MGMAT

7. Graph

Refer to MGMAT

8. Graph

Refer to MGMAT

9. Graph

Refer to MGMAT

A cartel is an explicit agreement among competing firms to fix prices, marketing, and production. The goal of a cartel is to increase individual members' profits by reducing competition. Although firms in many industries have tried to organize cartels, very few known cartels have lasted for more than 4 or 5 years. The main issue is that the members of a cartel all have an incentive to cheat and cut prices just a little in order to maximize their individual profits at the expense of profits of the cartel as a whole. True/False (one each) No cartel will last more than 100 years. As long as the members do not cheat, a cartel cannot be broken. An effective system for preventing members from cheating would not increase the likelihood that a cartel would survive in the long term. Private cartels are not legal in most countries. Cartels are inherently unstable and likely to fail in the long run. It is extremely difficult for competing firms to agree to fix prices, marketing, and production in the formation of a cartel.

True: The correct answer is E. I said F. False: The correct answer is C. Got right. The passage as a whole strongly suggests that few cartels last more than 4 or 5 years because of the economic incentive that members have to cheat. Option A - No cartel will last more than 100 years. This is much too strong of a statement to be logically inferred from "very few known cartels have lasted for more than 4 or 5 years." It could be that one or more known (or unknown) cartels has indeed lasted 100 years, even though only 4 to 5 years is typical. Option B - As long as the members do not cheat, a cartel cannot be broken. This is too strong of a statement to be inferred from "The main issue is that the members of a cartel all have an incentive to cheat and cut prices just a little in order to maximize their individual profits at the expense of profits of the cartel as a whole." There could be other issues. Perhaps new suppliers that are not part of the market enter the cartel, or perhaps the cartel's product is made technologically irrelevant. Option C - An effective system for preventing members from cheating would not increase the likelihood that a cartel would survive in the long-term. - Correct FALSE The passage says that the main issue is that the members of the cartel have an incentive to cheat, so an effective system for preventing cheating WOULD likely increase the likelihood that a cartel would survive in the long run. Option D - Private cartels are not legal in most countries. The passage does not discuss legality. Although this statement is likely true, it is not something that can be inferred from the passage. Option E - Cartels are inherently unstable and likely to fail in the long run. - Correct TRUE This can be directly inferred from "very few known cartels have lasted for more than 4 or 5 years" and "The main issue is that the members of a cartel all have an incentive to cheat and cut prices just a little in order to maximize their individual profits at the expense of profits of the cartel as a whole." The economic incentive to cheat is inherent in the nature of a cartel and makes it inherently unstable. Option F - It is extremely difficult for competing firms to agree to fix prices, marketing, and production in the formation of a cartel. This choice is tempting, but the passage does not discuss the difficulty of forming a cartel agreement. Although this statement is likely true in the real world, it is too extreme to infer language such as "extremely difficult" from the passage.

A factory produces one type of widget. This month, the factory raised the price of each widget to X% of the original price. However, the factory only sold Y% as many widgets as last month, and the total revenue from the sale of widgets was equal for last month and this month. In the table, identify the values of X and Y that are consistent with the information provided. Make only two selections, one in each column. X/Y (one each) 50 62.5 75 150 160 180

X: The correct answer is E. I said A. Y: The correct answer is B. I said C. The key to answering this question is finding the relationship between X and Y. First, create an equation that matches the information provided. Revenue from widget sales will equal the number of widgets sold times the price per widget. Let w be the original number of widgets sold and let p be the original price per widget. "X%" is the same as X/100; likewise, "Y%" is Y/100. If the revenues are equal for the two months, then: wp = (Y/100) × (w) × (X/100) × ( p) Notice that both sides of the equation contain w and p. Cancel out w and p (which are non-zero, by the logic of the real world, so you're allowed to divide them away). wp = (Y/100) × (w) × (X/100) × ( p) 1 = (Y/100) × (X/100) You can go further (to prove that XY = 10,000), but let's stay in "percent" land. What we have so far is that (Y/100) and (X/100) multiply together to 1. That is, they are reciprocals of each other. So let's save time. Divide every answer choice by 100, to convert it to the decimal equivalent of a percent. We get 0.50 0.625 0.75 1.5 1.6 1.8 Now, to determine which pairs multiply together to 1, notice that you'll need to pick one number smaller than 1 and the other number larger than 1. Which variable gets which? Since the factory "raised" the price to X%, we know that X% must be bigger than 100%, so X must be the one bigger than 1. Next, to check reciprocals quickly, see whether there's a quick fraction equivalent of each of these decimals. Fortunately, there is! 0.50 = 1/2 0.625 = 5/8 0.75 = 3/4 1.50 = 3/2 1.60 = 8/5 1.80 = 9/5 Now it's easy to spot the reciprocals. Know your eighths! (1/8 = 0.125, etc.) 5/8 × 8/5 = 1, so the correct percents are 62.5% and 160%. Again, X must be 160 and Y must be 62.5.